This invention relates generally to method and apparatus for finite element analysis and, more particularly, to a method and apparatus for generating a mesh of elements required for the analysis.
Finite element analysis (FEA) is a powerful numerical method for solving mathematical problems in engineering and physics. Finite element analysis is particularly relevant for determining the physical characteristics of an object such as a machine part, a hydraulic system, or printed circuit board. The fundamental concept of the finite element method is that any continuous physical characteristic, such as temperature, pressure, heat, or electric field, can be approximated by a discrete model composed of a set of piecewise continuous functions. These functions are defined over a finite number of subdomains of the object.
Finite element analysis today is typically carried out on a computer and consists of a three-step procedure: preprocessing, processing, and postprocessing. Preprocessing consists of taking data representing the object and generating therefrom a mesh of geometrical elements that cover the domain of the object. Processing is the analysis step, taking the element data and applying mathematical equations employed in the finite element method to solve for a matrix equation of the characteristic across the domain. Postprocessing provides results of the analysis to the user in a form that can be understood, such as a graphical representation of the characteristic by different colors that indicate the characteristic value across the domain.
The preprocessing step of generating an acceptable mesh for analysis is the primary bottleneck in employing finite element analysis. Present mesh generation methods can take from hours to days, depending upon the method employed. Typically, they require the user to pick nodes or vertices of the object in order to form regions in which elements will be generated. For example, the user manually divides the object into quadrilaterals on the computer screen to facilitate mesh generation. The choice of quadrilateral size and shape for optimum mesh generation, however, is not intuitive. The practicing engineer who is not an expert in finite element analysis is thus not likely to make the best choice. Moreover, once the regions are defined, the user must then specify a number of arbitrary vertical and horizontal connection points on the border of the region which are connected to generate a mesh within each region. The mesh that results may contain a number of elements that have poor aspect ratios, e.g., the ratio of the longest side of an element to its shortest side, that could skew the analysis. Only the expertise of the user can prevent this. For this reason, many companies employ expensive specialists to perform finite element analysis on their products. Examples of prior FEA methods that incorporate this type of preprocessing are the ANSYS FEA program from Swanson Analysis Systems, Inc., of Houston, PA; the NASTRAN FEA program from the MacNeal-Schwendler Corp. of Los Angeles, CA; the Patran FEA Program from PDA Engineering of Los Angeles, CA; and the Engineering Library For Modeling (ELM) from Fujitsu of America. These and other prior FEA methods require continued user input in generating the mesh of elements.
The prior method and similar computer-based FEA methods are certainly an improvement over previous manual methods. But these methods still require considerable time and expertise on the part of the user to generate a mesh. In the process of generating a mesh, the user is forced to concern himself with how to represent a given object domain by a collection of simple geometric subdomains suitable for analysis. This is a difficult and tedious manual task even for the expert.